On May 28, Tom Cruise is taking part in an unprecedented publicity stunt to trumpet his new sci-fi epic Edge of Tomorrow. The actor, along with co-star Emily Blunt, jetted to three fan premieres in three different cities in one day, beginning with a 7 a.m. red carpet call in London, a 2 p.m. screening in Paris and a 10 p.m. appearance in New York.

Cruise, one of Hollywood’s most diligent promoters, has been working overtime overseas because pre-release tracking for Edge of Tomorrow has been notably soft in the U.S. Warner Bros. in recent days has taken to reminding members of the press that Cruise remains a huge star overseas, even if his allure is somewhat muted from its heyday in America.

“Tom Cruise is seen as a big movie star internationally and when he goes out to promote a film, it is an event,” says Warner Bros. president of international distribution Veronika Kwan Vandenberg. “And films like Edge of Tomorrow with impressive action and heavy special-effects have a long track record of doing very well overseas.”

Still, Edge of Tomorrow is going to have to do monstrous business to make back its $178 million net production budget and $100 million-plus marketing spend. Moreover, it poses a crucial question for the 51-year-old actor: Outside of the Mission: Impossible franchise, can Cruise launch an original big-budget tentpole?

Edge of Tomorrow, directed by Doug Liman (The Bourne Identity, Mr. & Mrs. Smith), revolves around a military officer who, tasked with fighting alien invaders, finds himself living the same day over and over. The film rolls out in 27 foreign markets just as it premieres in Europe and New York, and a week ahead of its June 6 launch in North America. Warners is counting on strong opening numbers in major European, Latin America and Asian markets to generate positive headlines in the U.S., where tracking suggests Edge of Tomorrow may have trouble opening much past $25 million. If that’s the case, Edge could lose the weekend domestically to the $12 million-budgeted YA film adaptation The Fault in Our Stars, which would be a big perception problem.

Some believe part of the problem could be that the movie seems too similar to Cruise’s last film, 2013’s Oblivion, also a sci-fi tale. “Edge of Tomorrow is a fresh, exciting, great ride. Once people see it, there will be no confusion,” counters Vandenberg, adding that early reviews have been mostly glowing. The studio also has mounted an aggressive screening program around the world, both for exhibitors and the public.

Cruise’s recent films all have made far more offshore, but Edge of Tomorrow will need to do much bigger business than Oblivion, which cost less to make ($120 million) and opened outside of the competitive summer corridor. Launching in April 2013, Oblivion topped out at $286.2 million globally for Universal after earning $197.1 million overseas. Domestically, it debuted to $37.1 million on its way to grossing a lukewarm $89.1 million.

Phil Contrino, chief analyst for BoxOffice.com, questions whether Edge of Tomorrow would have done better in another play period.

“There are still really high expectations for Tom Cruise movies. It’s clear now he’s at a stage in his career where it’s safer for him to be in a known property like Mission: Impossible. For some reason, he’s having difficulty launching original movies,” Contrino says. “Edge of Tomorrow is sandwiched between X-Men: Days of Future Past and Transformers: Age of Extinction, a tough thing for any movie to overcome.”

Cruise’s last big original tentople was Steven Spielberg’s War of the Worlds, released just after his infamous 2005 couch-jumping incident on The Oprah Winfrey Show. The movie grossed $591.7 million globally, but some believe it didn't reach the heights it should have (it was beat by The Chronicles of Narnia: The Lion, the Witch and the Wardrobe, which earned $745 million). Cruise and his camp went on to weather several out-and-out disappointments – Lions for Lambs, Valkyrie and Knight & Day – but were heartened when Mission: Impossible – Ghost Protocol (2011) raked in $694.7 million globally upon its release in late 2011, becoming Cruise’s top-grossing film of all time (Mission: Impossible 5 is due out Dec. 25, 2015). But hopes dimmed again when the ensemble musical Rock of Ages and Jack Reacher underperformed, followed by Oblivion, which wasn’t a homerun.

Days of Future Past will be in its second weekend when Edge of Tomorrow starts rolling out internationally, but Edge will go directly against Disney’s female and family friendly Maleficent in many markets. The two films arguably target different audiences, but Maleficent boasts stronger tracking internationally.

Warners has an enviable track record when it comes to marketing tentpoles (many say marketing chief Sue Kroll is a fanboy at heart), including original properties such as Inception, so no one is ruling out a successful rescue operation. Last summer, Pacific Rim took in an impressive $309 million internationally after earning only $101.8 million in North America.

“The reviews for Edge of Tomorrow are going to help it, that’s for sure. It could hold up and find its audience,” says Contrino, reminding the biggest issue is the movie’s budget. “That’s a hindrance right there. If these budgets were kept in check, there would be a lot less of these conversations.”